Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #31771080 | C2 | semidirect |
| 3. #31771079 | C2 | semidirect |
| 4. #31770714 | C2 | semidirect |
| 5. #31770685 | C2 | semidirect |
| 6. #31770641 | C2 | semidirect |
| 7. #31770611 | C2 | semidirect |
| 8. #31770563 | C2 | semidirect |
| 9. #418×C269 | C2 | semidirect |
| 11. C2×#16864387 | C4 | semidirect |
| 17. D4×Dic269 | C22 | semidirect |
| 18. #22575415 | C22 | semidirect |
| 23. #22575386 | C22 | semidirect |
| 24. #22575384 | C22 | semidirect |
| 25. #22575375 | C22 | semidirect |
| 26. #22575363 | C22 | semidirect |
| 27. C8×Dic269 | C22 | semidirect |
| 31. #102×C269 | C22 | semidirect |
| 35. C2×D1076 | C2×C4 | semidirect |
| 39. #16864387 | C2×C4 | semidirect |
| 40. #16864387 | C2×C4 | semidirect |
| 41. C2×#14524130 | C2×C4 | semidirect |
| 55. C2×D4×C269 | C2×C4 | semidirect |
| 108. C269 | #2948 | semidirect |
| 117. #418 | D269 | semidirect |
| 138. #102 | C2×D269 | semidirect |
| 149. C2×D4 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864387 | 2 |
| #31771080 | 2 |
| #31771079 | 2 |
| #31770714 | 2 |
| #31770685 | 2 |
| #31770641 | 2 |
| #31770611 | 2 |
| #31770563 | 2 |
| #418×C269 | 2 |
| #2948 | 269 |